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A comment on The Connection That Changed Number Theory. Parent comment
If it is considered to be a prime, then you end up with a lot of theorems that start "for all primes p != 1" or "for all odd primes != 1".
If it is not considered to be a prime, you end up with other theorems that start "for all primes and 1" or "for all odd primes and 1".
There are more really important theorems in the former set than the latter set and so considering it to not be prime became the convention.
If it is considered to be a prime, then you end up with a lot of theorems that start "for all primes p != 1" or "for all odd primes != 1".
If it is not considered to be a prime, you end up with other theorems that start "for all primes and 1" or "for all odd primes and 1".
There are more really important theorems in the former set than the latter set and so considering it to not be prime became the convention.